Solve 6-{4-[x-(3x-1)+4]}=7x+10

$$6 - \{ 4 - [ x - ( 3 x - 1 ) + 4 ] \} = 7 x + 10$$

Solve for x

$$x=-\frac{1}{3}\approx -0.333333333$$

Steps for Solving Linear Equation

To find the opposite of 3x-1, find the opposite of each term.

$$6-\left(4-\left(x-3x-\left(-1\right)+4\right)\right)=7x+10$$

The opposite of -1 is 1.

$$6-\left(4-\left(x-3x+1+4\right)\right)=7x+10$$

Combine x and -3x to get -2x.

$$6-\left(4-\left(-2x+1+4\right)\right)=7x+10$$

Add 1 and 4 to get 5.

$$6-\left(4-\left(-2x+5\right)\right)=7x+10$$

To find the opposite of -2x+5, find the opposite of each term.

$$6-\left(4-\left(-2x\right)-5\right)=7x+10$$

The opposite of -2x is 2x.

$$6-\left(4+2x-5\right)=7x+10$$

Subtract 5 from 4 to get -1.

$$6-\left(-1+2x\right)=7x+10$$

To find the opposite of -1+2x, find the opposite of each term.

$$6-\left(-1\right)-2x=7x+10$$

The opposite of -1 is 1.

$$6+1-2x=7x+10$$

Add 6 and 1 to get 7.

$$7-2x=7x+10$$

Subtract 7x from both sides.

$$7-2x-7x=10$$

Combine -2x and -7x to get -9x.

$$7-9x=10$$

Subtract 7 from both sides.

$$-9x=10-7$$

Subtract 7 from 10 to get 3.

$$-9x=3$$

Divide both sides by -9.

$$x=\frac{3}{-9}$$

Reduce the fraction \frac{3}{-9} to lowest terms by extracting and canceling out 3.

$$x=-\frac{1}{3}$$